I'm also getting a knock on effect - yesterday over 600 unique visitors, 2,113 page hits, 26,271 overall hits and a whopping 817MB of bandwidth used - I'm actually hoping it'll drop off a little otherwise I'll have to either remove at least the .mov files or fork out for some alternate space or a greater bandwidth limit (currently 15 GB/month).
Edit: Should have said my normal unique visitors per day (say last month) was around 40.

lol

did you notice in my zoom that the shape in the last frame looks like an alien skull?

Thanks Inigo for the tip on using an orbit trap to mimic ambient occlusion lighting.
Here is a power 7 in Ultrafractal. The orbit trap makes a big difference.


Ultrafractal takes about two and a half minutes to produce this. I'm a bit less envious of the two-second GPU  versions now that I hear that they produce a fire hazard 

I'm glad Dave volunteered to test the second derivative distance formula. It's a bit of a monster, and probably too expensive, but I wonder how it performs.

Hi
I talked to Twinbee about this on deviantart and he told me to come here, so here I am.
Hi lycium.

I had one idea for why the standard Mandelbrotset behaves that assymmetric in this 3D-Variant.
Most likely, that is, because it already does so in the 2D-Version.
Well, nearly.
In the 2D-Version, z²+c produces only mirror-symmetries and relative to the zero-point, inside the caridode, one could say, it features "single-axial radial symmetry"
z³+c features double mirror symmetries or "2-axial radial symmetry"
z⁴+c features 3-axial radial symmetry and so on

zⁿ+c in general features an (n-1)-axial radial symmetry.

As things get twisted into higher dimensions, things with only one axis of symmetry start to look odd. they twist in a rather strange way and that happened to the z²+c-variant.

Though, I have a couple of ideas:
Right now, you basically use two totally unrelated angles and transform them in one and the same way to get your results.
What if you actually search for a relation between them?
One way to do this would be to interpret the two angles as complex unit vectors.

your formula for the angles then would be:

(r,theta,phi)ⁿ =
(rⁿ,2*pi*cos(arg(z))*n,2*pi*sin(arg(z))*n)

Other relations could be thinkable... though I only can give an example which probably does not work directly.
http://www.wolframalpha.com/input/?i=sqrt%28%28x%29^2%2B1%2F%28x%29^2%29%3D2
the idea here is that one angle always has to be the inverse of the other angle. But as the angles are real-valued, so that complex solutions wouldn't work, you only get four different values to work with.

A different way to get nice angular relations might be via the riemann-sphere.
Taking the radius as is but looking at where the iteration would have been found on the riemann-sphere, express it as the two angles (the radius of 1, as said is overwritten by the resulting radius) and plot the new position accordingly.
Though, as on the bottom of that sphere, you have zero and on the top you have infinity, this might lead to a different kind of distortion. - 3D but not as spherical as the original intention^^


A very exotic variant would be a weird clifford algebra without any real part.

Something like
i*i=-j
j*j=-e
e*e=0
i*e=j
j*e=i
i*j=e
i*j*e=e*e=0

no idea if that would actually describe something usable but it might be worth a try
Also, for that, you would probably need to figure out, if it at all works, how it works:
is j*i=i*j or not?

Ok, those where some random quick ideas. I hope, you like them

Akkara Leith pointed out to me the reason why some people are not getting the same formulas for my higher order non-trigonometric formulas. The reason is because I was using atan(y/x) instead of atan2(y,x) for my definition of theta. I have gone back and changed this to my original posts:
http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8426/#msg8426
http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8470/#msg8470

I am continuing to play with inverse Julia sets using the MIIM method. I was quite impressed with xenodreambuie's inverse Julia sets using this method. Earlier on this thread, he presented an interesting method for finding n² valid roots for any nth order formula. When I tried to implement this method, I found that sometimes some of the roots were still invalid, but with some minor modifications, I was able to consistently get all 16 unique valid roots for the 4th order formula. Here is an example of the 4th order inverse Julia set using MIIM. I still haven't implemented soft shading yet with my point cloud renderer, but I hope to add that soon.

 

Some early raytracing code for Mandelbulbs requiring the Optix SDK and CUDA tool kit to be found in this posting. Optix is an API for raytracing on CUDA capable graphics chips. It will run at interactive frame rates on a GTX260 graphics cards and better, however a binary patch is required to enable Optix on anything but Tesla and Quadro Fx cards (use google to find such hackery).

Dependencies are the Optix SDK by nVidia and the CUDA toolkit V2.3 or later - both available for free for Windows and Linux. Because .zip files can't be attached here, find the source code on the nVidia forums (need to register to download the attachment)

http://forums.nvidia.com/index.php?showtopic=150985&view=findpost&p=952165

Still, I am still very dissatisfied with the shading and lighting - it is hard to make out any surface detail. But it does ressemble the 8th order Mandelbulb. In my version I'd rather call it an ugly barnacle ball. But I am onto something. I only hacked on this for about 4 hours. I am still having issues with some transparently appearing pixels where there should be a solid. Also the way the surface normals are determined give the shading a weird and grainy look.

Let me know if my iteration formulas and parameters look correct. I mostly copied the approach by JosLeys in posts #355 and #397.

I'd love to learn how to implement the orbit traps correctly to simulate global illumination.

Christian